Nuprl Lemma : word-rel-append2
∀X:Type. ∀w1,x,y:(X + X) List. (word-rel(X;x;y) ⇒ word-rel(X;w1 @ x;w1 @ y))
Proof
Definitions occuring in Statement :
word-rel: word-rel(X;w1;w2),
append: as @ bs,
list: T List,
all: ∀x:A. B[x],
implies: P ⇒ Q,
union: left + right,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
word-rel: word-rel(X;w1;w2),
exists: ∃x:A. B[x],
member: t ∈ T,
and: P ∧ Q,
prop: ℙ,
cand: A c∧ B,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
so_apply: x[s],
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
exists_wf,
list_wf,
inverse-letters_wf,
equal_wf,
append_wf,
cons_wf,
nil_wf,
length_wf,
list_ind_cons_lemma,
list_ind_nil_lemma,
length-append,
word-rel_wf,
squash_wf,
true_wf,
iff_weakening_equal,
append_assoc
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
dependent_pairFormation,
hypothesisEquality,
sqequalRule,
cut,
introduction,
extract_by_obid,
isectElimination,
unionEquality,
cumulativity,
because_Cache,
hypothesis,
lambdaEquality,
productEquality,
applyLambdaEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
universeEquality,
independent_pairFormation,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
equalityUniverse,
levelHypothesis,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
independent_functionElimination
Latex:
\mforall{}X:Type. \mforall{}w1,x,y:(X + X) List. (word-rel(X;x;y) {}\mRightarrow{} word-rel(X;w1 @ x;w1 @ y))
Date html generated:
2017_10_05-AM-00_44_39
Last ObjectModification:
2017_07_28-AM-09_18_39
Theory : free!groups
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