### Nuprl Lemma : bool-deq-aux

`∀[a,b:𝔹].  uiff(a = b;↑a =b b)`

Proof

Definitions occuring in Statement :  eq_bool: `p =b q` assert: `↑b` bool: `𝔹` uiff: `uiff(P;Q)` uall: `∀[x:A]. B[x]` equal: `s = t ∈ T`
Definitions unfolded in proof :  uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` member: `t ∈ T` prop: `ℙ` uall: `∀[x:A]. B[x]` rev_implies: `P `` Q` implies: `P `` Q` iff: `P `⇐⇒` Q`
Lemmas referenced :  equal_wf bool_wf iff_weakening_uiff assert_wf eq_bool_wf assert_of_eq_bool assert_witness uiff_wf
Rules used in proof :  cut sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity independent_pairFormation isect_memberFormation hypothesis introduction extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality because_Cache addLevel productElimination independent_isectElimination independent_functionElimination cumulativity sqequalRule independent_pairEquality isect_memberEquality equalityTransitivity equalitySymmetry axiomEquality

Latex:
\mforall{}[a,b:\mBbbB{}].    uiff(a  =  b;\muparrow{}a  =b  b)

Date html generated: 2019_06_20-PM-00_31_59
Last ObjectModification: 2018_08_24-PM-10_58_41

Theory : equality!deciders

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