Nuprl Lemma : perm_f_inj
∀T:Type. ∀p:Perm(T). ∀x,y:T. (((p.f x) = (p.f y) ∈ T) ⇒ (x = y ∈ T))
Proof
Definitions occuring in Statement :
perm: Perm(T),
perm_f: p.f,
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
perm: Perm(T),
uall: ∀[x:A]. B[x],
biject: Bij(A;B;f),
and: P ∧ Q,
guard: {T},
uimplies: b supposing a,
inject: Inj(A;B;f)
Lemmas referenced :
perm_f_wf,
istype-universe,
perm_wf,
perm_properties,
perm_b_wf,
fun_with_inv_is_bij
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
hypothesis,
equalityIsType1,
inhabitedIsType,
hypothesisEquality,
applyEquality,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
setElimination,
rename,
because_Cache,
isectElimination,
universeIsType,
universeEquality,
productElimination,
independent_isectElimination,
independent_functionElimination
Latex:
\mforall{}T:Type. \mforall{}p:Perm(T). \mforall{}x,y:T. (((p.f x) = (p.f y)) {}\mRightarrow{} (x = y))
Date html generated:
2019_10_16-PM-01_00_42
Last ObjectModification:
2018_10_08-AM-11_01_13
Theory : perms_2
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