Nuprl Lemma : extend_perm_wf
∀n:ℕ. ∀p:Sym(n). (↑{n}(p) ∈ Sym(n + 1))
Proof
Definitions occuring in Statement :
extend_perm: ↑{n}(p),
sym_grp: Sym(n),
nat: ℕ,
all: ∀x:A. B[x],
member: t ∈ T,
add: n + m,
natural_number: $n
Definitions unfolded in proof :
extend_perm: ↑{n}(p),
sym_grp: Sym(n),
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat: ℕ,
perm: Perm(T),
implies: P ⇒ Q,
inv_funs: InvFuns(A;B;f;g),
and: P ∧ Q,
rev_implies: P ⇐ Q,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
tidentity: Id{T}
Lemmas referenced :
perm_wf,
int_seg_wf,
nat_wf,
mk_perm_wf_a,
extend_permf_wf,
perm_f_wf,
perm_b_wf,
equal_wf,
squash_wf,
true_wf,
istype-universe,
extend_permf_over_comp,
tidentity_wf,
subtype_rel_self,
iff_weakening_equal,
perm_properties,
identity_wf,
extend_permf_over_id
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation_alt,
cut,
sqequalHypSubstitution,
hypothesis,
universeIsType,
introduction,
extract_by_obid,
dependent_functionElimination,
thin,
isectElimination,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
addEquality,
because_Cache,
independent_functionElimination,
productElimination,
applyEquality,
lambdaEquality_alt,
imageElimination,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
universeEquality,
functionEquality,
imageMemberEquality,
baseClosed,
instantiate,
independent_isectElimination,
independent_pairFormation,
promote_hyp,
functionIsType
Latex:
\mforall{}n:\mBbbN{}. \mforall{}p:Sym(n). (\muparrow{}\{n\}(p) \mmember{} Sym(n + 1))
Date html generated:
2019_10_16-PM-00_59_54
Last ObjectModification:
2018_10_08-AM-09_14_27
Theory : perms_1
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