Nuprl Lemma : inv_perm_wf
∀T:Type. ∀p:Perm(T). (inv_perm(p) ∈ Perm(T))
Proof
Definitions occuring in Statement :
inv_perm: inv_perm(p),
perm: Perm(T),
all: ∀x:A. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
perm: Perm(T),
inv_perm: inv_perm(p),
uall: ∀[x:A]. B[x],
prop: ℙ,
mk_perm: mk_perm(f;b),
perm_f: p.f,
pi1: fst(t),
perm_b: p.b,
pi2: snd(t),
inv_funs: InvFuns(A;B;f;g),
and: P ∧ Q,
cand: A c∧ B
Lemmas referenced :
perm_wf,
perm_properties,
inv_funs_wf,
perm_f_wf,
perm_b_wf,
mk_perm_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
sqequalHypSubstitution,
hypothesis,
universeIsType,
introduction,
extract_by_obid,
dependent_functionElimination,
thin,
hypothesisEquality,
universeEquality,
setElimination,
rename,
dependent_set_memberEquality_alt,
isectElimination,
sqequalRule,
productElimination,
independent_pairFormation
Latex:
\mforall{}T:Type. \mforall{}p:Perm(T). (inv\_perm(p) \mmember{} Perm(T))
Date html generated:
2019_10_16-PM-00_58_49
Last ObjectModification:
2018_10_08-AM-09_46_32
Theory : perms_1
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