Nuprl Lemma : psub-same
∀a:formula(). (a ⊆ a ⇐⇒ True)
Proof
Definitions occuring in Statement :
psub: a ⊆ b,
formula: formula(),
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
true: True
Definitions unfolded in proof :
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
true: True,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
rev_implies: P ⇐ Q,
uimplies: b supposing a
Lemmas referenced :
psub_wf,
true_wf,
formula_wf,
psub_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
independent_pairFormation,
natural_numberEquality,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
because_Cache,
dependent_functionElimination,
independent_isectElimination
Latex:
\mforall{}a:formula(). (a \msubseteq{} a \mLeftarrow{}{}\mRightarrow{} True)
Date html generated:
2016_05_15-PM-07_13_42
Last ObjectModification:
2015_12_27-AM-11_30_34
Theory : general
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