Nuprl Lemma : mk_perm_eta_rw
∀T:Type. ∀p:Perm(T). (mk_perm(p.f;p.b) = p ∈ Perm(T))
Proof
Definitions occuring in Statement :
mk_perm: mk_perm(f;b),
perm: Perm(T),
perm_b: p.b,
perm_f: p.f,
all: ∀x:A. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
perm: Perm(T),
perm_f: p.f,
pi1: fst(t),
mk_perm: mk_perm(f;b),
perm_b: p.b,
pi2: snd(t),
uall: ∀[x:A]. B[x],
prop: ℙ,
perm_sig: perm_sig(T),
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
perm_wf,
perm_properties,
inv_funs_wf,
perm_f_wf,
perm_b_wf,
pair_eta_rw,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
hypothesis,
universeIsType,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
universeEquality,
dependent_set_memberEquality_alt,
sqequalRule,
isectElimination,
functionEquality,
lambdaEquality_alt,
because_Cache,
functionIsType,
inhabitedIsType,
setElimination,
rename
Latex:
\mforall{}T:Type. \mforall{}p:Perm(T). (mk\_perm(p.f;p.b) = p)
Date html generated:
2019_10_16-PM-00_58_46
Last ObjectModification:
2018_10_08-AM-09_46_35
Theory : perms_1
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