Nuprl Lemma : compose-flips-injection
∀n:ℕ. ∀L:(ℕn × ℕn) List. Inj(ℕn;ℕn;compose-flips(L))
Proof
Definitions occuring in Statement :
compose-flips: compose-flips(flips),
list: T List,
inject: Inj(A;B;f),
int_seg: {i..j-},
nat: ℕ,
all: ∀x:A. B[x],
product: x:A × B[x],
natural_number: $n
Definitions unfolded in proof :
prop: ℙ,
uimplies: b supposing a,
top: Top,
compose-flips: compose-flips(flips),
implies: P ⇒ Q,
so_apply: x[s],
so_lambda: λ2x.t[x],
nat: ℕ,
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Lemmas referenced :
nat_wf,
flip-injection,
flip_wf,
inject-compose,
reduce_cons_lemma,
map_cons_lemma,
identity-injection,
reduce_nil_lemma,
map_nil_lemma,
list_wf,
compose-flips_wf,
inject_wf,
int_seg_wf,
list_induction
Rules used in proof :
independent_isectElimination,
productElimination,
voidEquality,
voidElimination,
isect_memberEquality,
independent_functionElimination,
hypothesisEquality,
dependent_functionElimination,
lambdaEquality,
sqequalRule,
hypothesis,
because_Cache,
rename,
setElimination,
natural_numberEquality,
productEquality,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
thin,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}n:\mBbbN{}. \mforall{}L:(\mBbbN{}n \mtimes{} \mBbbN{}n) List. Inj(\mBbbN{}n;\mBbbN{}n;compose-flips(L))
Date html generated:
2018_05_21-PM-00_42_04
Last ObjectModification:
2017_12_10-PM-03_41_14
Theory : list_1
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